 | Space: Encyclopedia II - Space - Mathematical spaces
Space - Mathematical spaces
In mathematics, a space is a set, with some particular properties and usually some additional structure. It is not a formally defined concept as such, but a generic name for a number of similar concepts, most of which generalize some abstract properties of the physical concept of space.
In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume measurement leads to the concept of measure space.
As far as the concept of dimension is defined, this need not be 3: it can also be 0 (a point), 1 (a line), 2 (a plane), more than 3, and with some definitions, a non-integer value. Mathematicians often study general structures that hold regardless of the number of dimensions.
Kinds of mathematical spaces include:
- Banach space
- Euclidean space
- Hilbert space
- Metric space
- Probability space
- Projective space
- Topological space
- Vector space
Space - Physics and space
Space is one of the few fundamental quantities in physics meaning it can't be defined via other quantities because there is nothing more fundamental known at present. Thus, similar to the definition of other fundamental quantities (like time and mass), space is defined via measurement. Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time interval of 1/299792458 of a second (exact).
In classical physics, space is a three-dimensional Euclidean space where any position can be described using three coordinates. Relativistic physics examines spacetime rather than space; spacetime is modeled as a four-dimensional manifold, and currently, there are theories that can support up to eleven-dimensional spaces.
Before Einstein's work on relativistic physics, time and space were seen as independent dimensions. Einstein's work unified the two into spacetime. In spacetime, measurements of space and time are held to be relative to velocity.
Main article: Outer space
In astronomy, space refers collectively to the relatively empty parts of the universe. Any area outside the atmospheres of any celestial body can be considered 'space'. Although space is certainly spacious, it is now known to be far from empty, and filled with a tenuous plasma. In particular, the boundary between space and Earth's atmosphere is conventionally set at the Karman line.
Space - Spatial measurement
Main article: Measurement
The measurement of physical space has long been important. Geometry, the name given to the branch of mathematics which measures spatial relations, was popularised by the ancient Greeks, although earlier societies had developed measuring systems. The International System of Units, (SI), is now the most common system of units used in the measuring of space, and is almost universally used within science.
Geography is the branch of science concerned with identifying and describing the Earth, utilising spatial awareness to try and understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualisation purposes and to act as a locational device. Astronomy is the science involved with the observation, explanation and measuring of objects in outer space.
Geographical space is called land, and has a relation to ownership (in which space is seen as property). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behaviour, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming. Ownership of space is not restricted to land. Ownership of Airspace and of waters is decided internationally. Public space is a term used to define areas of land which are open to all, whilst private property is that area of land owned by an individual or company, for their own use and pleasure.
Other related archivesAirspace, Astronomy, Banach space, Cartography, Critique of Pure Reason, Earth, Earth's atmosphere, Environments, Euclidean space, Geography, Geometry, Gottfried Leibniz, Henri Poincaré, Hilbert space, Immanuel Kant, International System of Units, Isaac Newton, Karman line, Measurement, Metric space, Outer space, Philosophy of space and time, Probability space, Projective space, Public space, Relativistic physics, Space exploration, Spatial planning, Topological space, Topology, Vector space, a priori, abstract, agoraphobia, amodal perception, ancient Greeks, anxiety, architecture, astronomy, atmospheres, bucket argument, celestial body, classical physics, claustrophobia, conceptual, coordinates, dimension, dimensions, distance traveled by light in a vacuum, events, farming, framework, fundamental, hunting, land, manifold, mass, mathematics, measure space, measurement, measurements, meter, metric space, number, object permanence, objects, ontological, outer space, ownership, perception, philosophical, physics, plasma, private property, property, psychology, quantify, science, self preservation, set, spacetime, sphere-world, structure, substances, time, universe, vector space, waters
 Adapted from the Wikipedia article "Mathematical spaces", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
